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Title: Power-law connections: From Zipf to Heaps and beyond

Abstract

In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ► The large-ensemble asymptotic statistics of rank distributions are explored. ► Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ► Associated oligarchy sizes and induced innovation rates are analyzed. ► General elemental statistical connections are established. ► The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled.

Authors:
 [1];  [2];  [3]
  1. Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel)
  2. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019 (United States)
  3. (United States)
Publication Date:
OSTI Identifier:
22220712
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 332; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DISTRIBUTION; PHASE TRANSFORMATIONS; PROBABILITY; STATISTICS

Citation Formats

Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il, Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu, and Department of Chemistry, Princeton University, Princeton, NJ 08544. Power-law connections: From Zipf to Heaps and beyond. United States: N. p., 2013. Web. doi:10.1016/J.AOP.2013.01.013.
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il, Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu, & Department of Chemistry, Princeton University, Princeton, NJ 08544. Power-law connections: From Zipf to Heaps and beyond. United States. doi:10.1016/J.AOP.2013.01.013.
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il, Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu, and Department of Chemistry, Princeton University, Princeton, NJ 08544. Wed . "Power-law connections: From Zipf to Heaps and beyond". United States. doi:10.1016/J.AOP.2013.01.013.
@article{osti_22220712,
title = {Power-law connections: From Zipf to Heaps and beyond},
author = {Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il and Cohen, Morrel H., E-mail: mcohen@physics.rutgers.edu and Department of Chemistry, Princeton University, Princeton, NJ 08544},
abstractNote = {In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ► The large-ensemble asymptotic statistics of rank distributions are explored. ► Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ► Associated oligarchy sizes and induced innovation rates are analyzed. ► General elemental statistical connections are established. ► The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled.},
doi = {10.1016/J.AOP.2013.01.013},
journal = {Annals of Physics (New York)},
number = ,
volume = 332,
place = {United States},
year = {Wed May 15 00:00:00 EDT 2013},
month = {Wed May 15 00:00:00 EDT 2013}
}
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